2x(x+14)=(x-3)(x-3)

Solution for 2x(x+14)=(x-3)(x-3) equation:

2x(x+14)=(x-3)(x-3)

We move all terms to the left:

2x(x+14)-((x-3)(x-3))=0

We multiply parentheses

2x^2+28x-((x-3)(x-3))=0

We multiply parentheses ..

2x^2-((+x^2-3x-3x+9))+28x=0


We calculate terms in parentheses: -((+x^2-3x-3x+9)), so:

(+x^2-3x-3x+9)

We get rid of parentheses

x^2-3x-3x+9

We add all the numbers together, and all the variables

x^2-6x+9

Back to the equation:

-(x^2-6x+9)


We add all the numbers together, and all the variables

2x^2+28x-(x^2-6x+9)=0

We get rid of parentheses

2x^2-x^2+28x+6x-9=0

We add all the numbers together, and all the variables

x^2+34x-9=0

a = 1; b = 34; c = -9;
Δ = b2-4ac
Δ = 342-4·1·(-9)
Δ = 1192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1192}=\sqrt{4*298}=\sqrt{4}*\sqrt{298}=2\sqrt{298}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{298}}{2*1}=\frac{-34-2\sqrt{298}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{298}}{2*1}=\frac{-34+2\sqrt{298}}{2}
$